Electricity Storage for Intermittent Renewable Sources

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Cite this: Energy Environ. Sci., 2012, 5, 7151 www.rsc.org/ees PAPER Electricity storage for intermittent renewable sources

Jason Rugolo and Michael J. Aziz*

Received 1st September 2011, Accepted 12th March 2012 DOI: 10.1039/c2ee02542f

With sufficient electricity storage capacity, any power production profile may be mapped onto any desired supply profile. We present a framework to determine the required storage power as a function of time for any power production profile, supply profile, and targeted system efficiency, given the loss characteristics of the storage system. We apply the framework to the electrochemical storage of intermittent renewable power, employing a simplifying linear response approximation that permits the entire efficiency behavior of the system to be described by a single scalar figure of merit—the discharge power capacity. We consider three exemplary grid supply scenarios: constant, grid-minus-baseload, and square wave; and two different production scenarios: wind with a capacity factor 32.5%, and solar photovoltaic (PV) with a capacity factor of 14%. For each of these six combinations of scenarios, the storage energy and discharge power capacity requirements are found for a range of system efficiencies. Significantly diminishing efficiency returns are found on increasing the discharge power capacity. Solid-electrode batteries are shown to have two orders of magnitude too little energy to power ratio to be well suited to the storage of intermittent renewable power.

1 Introduction the wind is blowing or the sun is shining. The only way to turn naturally ﬂuctuating wind or PV electricity into a dispatchable The intermittency of renewable power sources such as wind and electricity source (see Fig. 1) is to have some other dispatchable photovoltaic (PV) presents a major obstacle to their extensive 1,2 form of electrical energy to take up the slack (a so-called penetration into the grid. The developed world has become ‘‘balancing capacity’’). accustomed to reliable, on-demand electricity; most of its pop- The intermittency of the renewable sources added to the grid ulation simply would not accept access to electricity only when up to the present time have been balanced by the dispatchable forms of electricity (mainly natural gas peaking plants) that

Harvard School of Engineering and Applied Sciences, 29 Oxford St., Cambridge, MA 02138, USA. E-mail: [email protected]; Fax: +1 (617) 495-9837; Tel: +1 (617) 495-9884

Broader context The intermittency of renewable power sources such as wind and photovoltaic presents a major obstacle to their extensive penetration into the grid. Large scale electrical energy storage is a potential solution to this problem. We present a framework to determine the required storage power as a function of time for any power production profile, supply profile, and specified system efficiency, given the loss characteristics of the storage system, which operates over a distribution of instantaneous efficiencies depending on the instantaneous power. We apply the framework to the electrochemical storage of intermittent renewable power, employing a simplifying linear response approximation that permits the entire efficiency behavior of the system to be described by a single scalar figure of merit—the discharge power capacity. We consider three exemplary grid supply scenarios for a wind and a photovoltaic production scenario. In each case we find the storage energy and discharge power capacity requirements. Significantly diminishing efficiency returns are found on increasing the discharge power capacity much beyond 1 MW of storage per MW of nameplate generation. Solid-electrode batteries are shown to have two orders of magnitude too little energy to power ratio to be well suited to the storage of intermittent renewable power.

This journal is ª The Royal Society of Chemistry 2012 Energy Environ. Sci., 2012, 5, 7151–7160 | 7151 Fig. 1 (A) The normalized shape of wind power calculated from real wind speed data in Wilhelminadorp, Netherlands, by applying the power curve for a GE 1.5MW turbine.3,4,5 (B) The normalized shape of solar PV power output in January in Boston, MA, USA.6 (C) The normalized shape of electricity demand in the UK from the National Grid website.7 N.B. The data shown are a 500 h subset of the larger range used for normalization. currently sit ready to produce when the price incentivizes them to demand in becalmed locations. To solve the majority of the do so.8 To integrate intermittent sources beyond some level of problem with this approach, though, appears quite difficult. penetration, the grid will require new balancing capacity.9 The Nationwide transmission capacity would have to be overbuilt, amount of backup dispatchable power required to balance an over very long distances, driving the transmission capacity factor intermittent source is unclear, especially in light of the compli- down substantially. This is an expensive proposition which, when cations associated with transmission availability. Preliminary added to the already-high price tag of intermittent renewable estimates of the cost of integration vary from 0.006 USD production, might drive the price of intermittent renewables (kW h)1 for 20% penetration to 0.0018 USD (kW h)1 for 4% unacceptably high. Additionally, a grid re-engineering of suffi- penetration.8 Even the low-cost estimates make integration cient magnitude may be indefinitely delayed because it would a difficult question.† require massive capital investments and coordination among The potential solutions to the integration problem have their federal, state, and local governments, private corporations, and own significant drawbacks.10 Adding natural gas peaking private land owners. Certainly something must be done about the capacity results in a paradox. A significant motivation for adding intermittency if President Obama’s stated goal of 80% clean renewables in the first place is to lower the carbon intensity of energy penetration by 2035 is to be met. electricity production. By requiring additional natural gas as a backup to smoothen renewable production, a limit is set on the 2 Electricity storage as a potential solution fraction of electricity that can come from the carbon-free sources.‡ Electricity storage (ES) represents a large class of technologies It has been suggested that spatially uncorrelated wind elec- with the potential to address the intermittency problem without tricity production may have a balancing effect of its own. Elec- a significant marginal carbon footprint compared to fossil fuel tricity can be overproduced where the wind is blowing and be combustion. Many types of ES exist, all which have the common transmitted some distance of order the uncorrelated wind characteristic that they convert electricity into stored energy in 11 distance (more than several hundred kilometers ) to meet some medium through a conversion device, and then, either through the same device or another, convert that stored energy back into electricity, while losing some in the round trip due to † An upper limit on the integration cost is the cost of an equal amount of dissipative processes. Among them are pumped hydro, dispatchable power for times when the wind is dead or the sun is down. compressed air, flow batteries, solid-electrode batteries, liquid ‡ This limit is complicated, but in the case of 100% intermittent batteries, regenerative fuel cells, and hybrid electrochemical cells. renewables with natural gas backup and no curtailment, natural gas electricity would constitute one minus the average intermittent Each of these applications provides the opportunity for a rich renewable capacity factor (something certainly more than half). discussion, with many unique characteristics affecting the

7152 | Energy Environ. Sci., 2012, 5, 7151–7160 This journal is ª The Royal Society of Chemistry 2012 ultimate conclusion of whether or not the application’s value can illustrative examples); this power is either delivered to the storage overcome the cost of storage and provide an acceptable profit. system or to the grid, or is lost by dissipation. PR(t) is set by the The economic question is very complicated, as it requires the energy resource and the production system. Only the shape of intersection of a detailed technical understanding of the storage this profile matters, so for simplicity this function is normalized device with a profound understanding of the markets, most of to unity at its peak value, e.g. the nameplate power production which have yet to be demonstrated on any significant scale.x An capacity of the wind turbine or PV array. in-depth economic analysis requires answers to questions such as The supply profile SU(t) is the time-structure of the power that how much storage is required to match a given intermittent the producer delivers to the grid; it, too, is normalized to unity at source, what efficiency can be expected, and what are the costs. its peak value. This represents a specific scenario for how the We briefly discuss each of these in turn. producer intends to deliver power to the consumer. The supply The required amount of a storage technology depends on the profile, combined with a model of the time-dependence of the producer’s choice for the time-structure of the power to be electricity price, determines the revenue earned by the production supplied. For example, the supplied power can be designed to and ES system. Among the possible supply profiles are constant provide constant output, follow the load, or provide constant output, load-following (Fig. 1C), square wave of various dura- output only when demand and prices are high. There is no unique tion and phase, variable profit-maximizing schemes, and many answer to this supply shape question because it can depend others including combinations of these. largely on the local regulatory framework or incentive structures In the absence of dissipative losses, one would scale the supply surrounding a specific project. output such that the area under SU(t) equals the area under The efficiency that can be expected is a surprisingly compli- PR(t). But losses cause the total energy supplied to be less than cated question. Losses are generally dependent on the instanta- the total energy produced by a factor that is not knowable neous system power and the unique properties of the specific a priori because it depends on the detailed behavior of ST(t)in storage system, including its chosen size as specified by attributes conjunction with the detailed behavior of the storage technology. such as peak power capacity and total energy storage capacity. To account for this discrepancy we introduce a scalar, a, that For a chosen temporal supply structure and a specific storage scales SU(t) vertically. The actual power supplied is a$SU(t); a is system, one may calculate a histogram of the hours at which the determined by the criterion that the area under a$SU(t) is less storage system suffers various amounts of loss. The average than the area under PR(t) by the amount of energy lost through system efficiency can then be calculated once this loss distribu- storage. tion is determined. The ES system must do whatever is necessary in order to Rough costs of storage depend strongly on the amount of ensure that the power produced plus the storage power yields the energy and power capacity purchased. Deciding on how much of desired power supplied: either to purchase depends on expected revenue, which is inti- mately related to the chosen time-structure of the power to be ST(t) ¼ a$SU(t) PR(t) (1) supplied, and how much energy is lost in the storage process. The energy and power capacity decision is thus characterized by Whereas SU(t) and PR(t) are normalized functions assumed to having several co-dependent parts. be pre-determined, we must find a way to solve for a such that the A full economic model is beyond the scope of this work and energy balance is correct. Calculating a requires knowledge of may not yet be possible. However, we expect a generic, the storage system’s loss rate as a function of time, Ploss(t), which economically focused consideration of the technical aspect of ES depends on the instantaneous storage power, ST(t), among other { to be useful for those who may make detailed economic models things, depending on the technology. This calculation must be in the future. Here, we develop a broadly applicable theoretical done recursively such that ST(t) and a converge to a mathemat- framework that facilitates the detailed discussion of ES ically consistent solution. D ¼ prospects. The total energy lost over a long time period t t2 t1 is the integral of Ploss(t) over that time period: ð t2 3 Electricity storage power functions Dt ¼ ð Þ Eloss Ploss t dt (2) t 3.1 Production, storage, and supply functions 1 The required magnitude of Dt will be discussed shortly. The function central to our analysis is the power of the ES system Requiring the net amount of energy stored over this time period as a function of time, which we denote ST(t) (for storage power). to be negligibly small, the energy dissipated must also be the ST(t) is positive when the storage system is delivering energy to difference between the energy produced and that supplied: the consumer (discharging) and it is negative during over- production when energy is being added to the storage system (charging). The expected power production profile PR(t) is the power produced by the wind turbine or solar panel (Fig. 1A,B shows { ‘‘Other things’’ may include the state of charge, side reactions, de-activation of catalyst, ageing of other components (membranes, etc.), local temperature fluctuations, balance of plant losses, and many x The lack of wide adoption of electricity storage is most commonly others. These are typically a function of ST(t) and its history, although attributed to the cost of storage being too high, but this may change in not always (as with local temperature). In particular, extension to the near future because of the intense research and development include state of charge dependence seems like an interesting and currently focused on making ES better and cheaper. tractable direction for future research.

This journal is ª The Royal Society of Chemistry 2012 Energy Environ. Sci., 2012, 5, 7151–7160 | 7153 ð ð t2 t2 Dt ¼ ð Þ ð Þ Eloss PR t dt a SU t dt (3) t1 t1

Dt We now equate the two expressions for Eloss (eqn (2) and (3)) to obtain a second relationship, in addition to eqn (1), between ST(t) and a. These equations comprise a closed set that can be solved numerically for ST(t) and a, so long as Ploss(t) is known and depends only on ST(t) and its history. For the results to be informative, Dt must be long enough that the behavior of the system has converged onto some average characteristic behavior. A good proxy for meeting this criterion is to track the behavior of the production capacity factor with increasing Dt. Once the production capacity factor is observed to approach an average value, it is reasonable to assume that, for power proﬁles with the same capacity factor, the statistically signiﬁcant variability in the system has been accounted for. For Fig. 2 Hydrogen-chlorine regenerative fuel cell behavior exemplifying Dt the calculations presented later, was chosen to be 744 h (about constant-activity electrochemical cell. In red is the cell potential and in 1 month). blue is the power density (p ¼ E(i)$i). The zero-current potential in this particular example is 1.36 V (horizontal dotted line), which is the equi-

librium potential under standard conditions for the H2(g) and Cl2(g) 3.2 The dissipated power, Ploss(t) couple (producing HCl(aq)). The solid lines represent realistic fuel cell behavior, the dashed lines represent a linear approximation to the The power loss function P (t) describes the power being dissi- loss voltage-current relationship, and the dotted lines represent the thermo- pated within the storage system as unwanted outputs such as dynamic limit. The total overpotential is indicated by the red arrow as the heat. This function, which depends on many technology-specific voltage difference between E(i) and Eeq. The corresponding power loss is parameters, is one of the key technological considerations indicated by the blue arrow. affecting energy storage prospects. Each storage technology has differing loss characteristics. consumed if the operation were thermodynamically reversible Compressed air storage, for example, uses a compressor to (i.e. no dissipation). The power density, p [mW cm2], is the cell compress air for storage, and delivers the energy by letting the air potential E(i) [V] times the current density i [mA cm2]: expand through a turbine. The compressor efficiency depends on ¼ $ the efficiency of the motor that turns the compressor, as well as p E(i) i. (4) on the state of charge of the reservoir and on all of the dissipative losses in the compressor system. The motor efficiency and the dissipation within the compressor both depend on the The overpotentials subtract from the reversible potential, compression rate, which is a function of the power during which is also called the equilibrium potential, Eeq. In the ideal charging and the number of compressors deployed for the job. (loss-free) case of zero overpotentials, the power density would Similarly, during discharge, the power loss in the turbine is be dependent on the characteristics of the turbine, the number of p ¼ E $i. (5) turbines deployed, and the rate at which air flows through ideal eq a turbine to create electricity. The engineer is able to pin down The loss power density is the difference between pideal and p: the dependence of the power loss function on the relevant engineering and operating parameters in the system. ploss ¼ pideal p (6) There are similarly complicated loss functions for each storage technology class. Electrochemical cells are among the simplest. ploss and Ploss are related to each other by the cell area, as are An electrochemical cell has several loss mechanisms (called ST(t) and p: overpotentials) that contribute to the total overall loss. Namely, STðtÞ there is an activation overpotential for each of two electrodes, an p ¼ ; (7) ohmic resistance overpotential, and a mass transport over- A potential, all of which are functions of the current density.k PlossðtÞ These combine to make the cell potential deviate from the ploss ¼ : (8) A equilibrium potential during operation. The behavior of a typical electrochemical cell is shown in Fig. 2. Because each of the losses is a function of current density,itis The power dissipated in any electrochemical cell during important to note that the loss function depends on the total operation represents a comparison of the energy produced or working area of electrochemical cell in operation.** consumed by the cell to the energy that would be produced or ** Ultimately, then, the efficiency depends on capital expenditure. For k One may also add a weakly time-dependent ‘‘degradation’’ electrochemical cells, the efficiency can get arbitrarily close to 100% as overpotential, which catches all of the characteristics of diminishing the installed cell area gets arbitrarily large. The cell area would be performance over time. In the present work, we ignore these slow effects. a major capital cost parameter in a full economic model.

7154 | Energy Environ. Sci., 2012, 5, 7151–7160 This journal is ª The Royal Society of Chemistry 2012 The example shown in Fig. 2 is that of a hydrogen-chlorine regenerative fuel cell.†† This belongs to the larger class of constant- activity electrochemical cells, in which the reactants and products are maintained at constant activity; hence Eeq does not depend on the state of charge.‡‡ The difference between the equilibrium potential and the cell potential is the magnitude of the voltage loss (the total overpotential), and is made up of the four aforemen- tioned overpotentials. One may see that the loss increases signiﬁ- cantly as a function of current density, and in the galvanic direction the loss ultimately consumes 100% of the cell power.

If Ploss(ST(t)) is known, one can solve for ST(t), which fully speciﬁes the prospective ES system. From ST(t), one may derive the system’s state of charge Q(t), the efﬁciency distribution, the amount of energy lost, the maximum stored energy required, the maximum discharge power required, and the general behavior that would be required of the storage system for the chosen delivery scenario. This information is essential for a rational storage selection process. Fig. 3 Lost power vs. storage power for different values of the maximum This is the central result of this paper. possible discharge power, PA. Both power variables are normalized by the source nameplate power.

3.3 The linear potential approximation potential as functions of the power density. Defining the maximum discharge power density P and the current density iP The linear potential approximation is a good approximation for at maximum power as most electrochemical cells (with the notable exception of the E2 hydrogen-oxygen fuel cell) and it greatly simplifies the analysis Ph eq r (10) and the ensuing discussion. The actual cell potential illustrated in 4 Fig. 2 is more nonlinear than would be expected from a real and system—it was chosen that way for illustrative purposes. The Eeq iPh (11) approximation is particularly good for high-efficiency operation 2r at low current density, where most cells would be expected to operate for longer duration ES applications. Hence we approx- leads to the following compact forms for i(p) and E(p): rffiffiffiffiffiffiffiffiffiffiffiffiffi imate the potential vs. current density as a straight line, permit- p iðpÞ¼iP 1 1 (12) ting an analytical solution for Ploss(t). P Although in any calculation with high financial stakes one should attempt to model real-world behavior as closely as 0 rffiffiffiffiffiffiffiffiffiffiffiffiffi1 p possible by using a more accurate potential function, even in this B1 þ 1 C B PC case the linear model remains valuable in showing the generic EðpÞ¼Eeq@ A (13) 2 behavior of an ES system. The cell potential as a function of current density is thus described by

We now solve for Ploss(ST(t)) using eqn (5)–(8): E(i) ¼ Eeq ri, (9) rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! STðtÞ PlossðtÞ¼2PA 1 1 STðtÞ: (14) where Eeq is the equilibrium potential in volts, i is the current PA density in mA cm2, and r is the loss parameter in kU cm2. The value of r for the linear approximation curve in Fig. 2 is 0.001 kU This equation shows that for constant-activity electrochemical cm2, which is a presently achievable value for this parameter.12 cells under the linear potential approximation, the only parameter The power density p can be written solely as a function of necessary to characterize the power dissipated versus time for the current density by substituting eqn (9) into eqn (4). p can also storage system is the maximum possible discharge power, PA. be written solely as a function of cell potential by inverting eqn The lost power vs. instantaneous power is plotted for various (9) to find i(E), and then substituting i(E) into eqn (4). These values of this parameter in Fig. 3. As PA is increased, the power manipulations lead to quadratic expressions for p(i) and p(E), loss for any given ST(t) scenario decreases. With this expression respectively. These quadratic equations can be inverted to for Ploss(ST) for a storage technology characterized by PA, the set obtain expressions for both the current density and the of eqn (1), (2), and (3) forms a closed set from which ST(t) and a can be calculated for any given choice of PR(t) and SU(t). †† The hydrogen-oxygen fuel cell is atypical due to the enormous The product PA in eqn (14) determines the overall efficiency nonlinear oxygen electrode overpotential loss, which makes it behavior.xx Because PA may be chosen freely, we next ask what unsuitable for efficient ES, and so it is ignored in this work. ‡‡ Varying-activity cells such as solid-electrode batteries and flow batteries have a Ploss that depends additionally on the state of charge, xx P depends on which technology is installed, and A is how much of it is which must be calculated from the history of ST(t). installed.

This journal is ª The Royal Society of Chemistry 2012 Energy Environ. Sci., 2012, 5, 7151–7160 | 7155 Fig. 4 Mapping wind and solar PV sources to constant power output with a specified average system efficiency of havg ¼ 0.85. (A) Storage power, ST(t), for the wind production profile PR(t) shown in Fig. 1A (capacity factor 0.325), that is required for converting wind to constant output SU(t) ¼ 1. The results are a ¼ 0.276 and PA ¼ 0.480 as discussed in the text. (B) ST(t) for the PV PR(t) shown in Fig. 1B (capacity factor 0.14), that is required for converting PV to constant SU(t) ¼ 1. The results are a ¼ 0.119 and PA ¼ 0.568 as discussed in the text. Power is normalized by source nameplate power capacity.

value of PA is necessary for the overall system efficiency, havg,to renewable capacity, and to curtail the energy produced when reach a targeted value. The average system efficiency is defined as production overloads the available transmission.13 In cases the energy supplied divided by the energy produced over some where limited transmission is already available, it may be much time period: easier to build on-site storage than to go through the permitting Ð process for additional transmission. A constant SU(t) has the a t2 SUðtÞdt h ¼ Ð t1 : (15) potential to best utilize available transmission, because one could avg t2 PRðtÞdt t1 design the system such that transmission is always operating at full capacity. What storage power and energy capacities are h Setting avg to a target value, e.g. 85%, enables the calculation required to map wind and PV production profiles onto P of the value of A needed to achieve that average efficiency, for a constant supply profile at a specified system efficiency? h a given PR(t) and choice of SU(t). A plot of avg as a function of Fig. 4 shows the resulting storage functions for the wind-to- P A provides insight into the cost-benefit trade-off of installing constant and solar-to-constant production cases. Because the more storage power. peak production power has been normalized to unity, all power numbers presented here are as fractions of the peak, or 4 Production and supply scenarios nameplate, power of the real system. Through a storage system Here we examine the storage power and energy requirements for with 85% system efficiency, a 1 MW nameplate wind turbine several production and supply scenarios and a range of system with a capacity factor of 0.325 must output a constant 0.85 ¼ ¼ efficiencies. The two production scenarios are the intermittent 0.325 0.276 MW. This implies a 0.276 and our calculations wind and PV temporal profiles shown in Fig. 1 A, B. The first, find that the required storage hardware has a peak discharge P ¼ and simplest, supply scenario is a system supplying constant power capacity of A 0.480 times the turbine nameplate. power from either of these intermittent sources. We subsequently Likewise, for PV levelized through a storage system with 85% consider a temporal supply structure that follows grid daytime system efficiency, a 1 MW peak PV array with a capacity factor ¼ demand, and a square wave that supplies all of its power during of 0.14 must output a constant 0.85 0.14 0.119 MW. This ¼ a five-hour period of peak demand. implies a 0.119 and the required storage hardware has a peak discharge power capacity of PA ¼ 0.568 times the PV peak power. The dashed lines in the figures, showing the constant 4.1 Constant power from intermittent wind or PV power supplied in each case (a SU(t)), are consistent with the The low capacity factors of intermittent renewables cause capacity factors of 0.325 for the wind example and 0.14 for the a difficult transmission problem. If enough transmission is built PV example. to transmit the peak power capacity of an intermittent power Finally, we determine the energy capacity of the storage source, on average the utilized fraction of the transmission needed for these scenarios. First, the state of charge (SOC), Q(t), capacity is the production capacity factor, which ranges from 20 must be determined as a function of time. This is done by inte- to 50% for wind and from 10 to 20% for solar PV. In some cases, grating the current from eqn (12) from an arbitrarily chosen time this has led to the decision to build less transmission than origin:

7156 | Energy Environ. Sci., 2012, 5, 7151–7160 This journal is ª The Royal Society of Chemistry 2012 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 ð ð À Á t t 0 À À 0 ÁÁ 0 ST t 0 ð Þ¼ ¼ @ A Q t A i p t dt iPA 1 1 P dt (16) 0 0 A

The SOC varies with time in much the same way as the powers do. The total charge capacity required by the storage system is the difference between the absolute maximum SOC and the absolute minimum SOC over all time. Because we need to project the future from data covering a limited time span in the past, we must ensure that this time span is long enough to make reasonably reliable predictions, e.g. that potential extended charge or discharge cycles have been included in the analysis. For example, for wind we must make sure to include a characteristic dead spell, which requires the storage of a large amount of charge. A good proxy for this condition should be tracking the capacity factor as the period of integration increases, as discussed above. To calculate the energy capacity,{{ one must multiply the charge capacity by the equilibrium potential, Eeq. When we perform this calculation we find that the energy capacity required for the wind-to-constant scenario of Fig. 4A is 49 h, whereas the energy capacity required for the solar-to- constant scenario of Fig. 4B is 14.5 h—i.e., for 1 MW nameplate wind and PV systems, 49 MWh and 14.5 MWh, respectively. Wind outproduces solar by the ratio of their capacity factors—in these scenarios, 0.325/0.14 ¼ 2.32. This is not as large a ratio as the ratio of the required energy, which is 49/14.5 ¼ 3.4. Wind requires more energy capacity in these scenarios, even after accounting for its increased production capacity factor, because there are longer periods of time when the wind does not blow than there are when the sun does not shine, and the storage must be there to take up the slack. These long dead periods create a particularly large energy capacity burden on a storage system. Fig. 5 (A) The system efficiency, havg, as a function of the maximum The required storage power and energy depend on the desired storage discharge power, PA, for mapping the wind (black lines) and solar (red lines) scenarios in Fig. 1 to a constant output. Power is system efficiency. Fig. 5A shows the system efficiency, havg,as a function of the maximum discharge power PA for both the normalized by source nameplate power capacity. (B) The energy capac- h P wind- and solar-to-constant scenarios in Fig. 4. As we increase ities required for the above avg- A combinations. The crosses mark 85% efficiency, corresponding to the ST(t) curves in Fig. 4. the system efficiency specification, the necessary maximum power (PA) increases in order to achieve more efficient cell operation. As the system efficiency approaches the limit of 100%, Both of these storage scenarios permit up to 100% trans- we see diminishing returns on increasing the maximum discharge mission capacity factor. Thus, for any new installation of inter- power. Fig. 5B shows the relationship between the required mittent power, one may consider buying less transmission and energy capacity and havg for the same scenarios. Note that the utilizing it completely, enabled by buying the amount of storage relationship is indirect. The specified system efficiency deter- determined above. Also, for existing intermittent power instal- mines PA, as in Fig. 5A. Then, for a given ST(t) scenario, any lations that have reached their transmission capacity, storage havg-PA pair determines a corresponding energy capacity may be particularly valuable. By adding the amount of storage requirement, and this is plotted in Fig. 5B. determined above, the production capacity can be expanded From these figures, it appears that for the constant supply about three times in this wind scenario, and about seven times in scenario, storage of wind is much more demanding than storage this PV scenario, without upgrading the transmission. of solar PV from a storage energy perspective and slightly less demanding from a storage power perspective for most efficiencies. We conjecture that more detailed studies will lead to this 4.2 Time-dependent supply scenarios conclusion. Note that, for flow batteries and regenerative fuel In the same way that the calculations reported above were per- cells, installing extra energy capacity means installing larger formed for a constant supply profile SU(t) ¼ 1, one can evaluate tanks and more reactants. Chemistries exist for which this is the storage power and energy requirements for any desired much less expensive than installing more power capacity. supply profile. SU(t) may vary widely within the realm of interest. An SU(t) profile that supplies power only during the peak consumption hours of the day, when the electricity price is {{ The energy capacity would more appropriately be called the reversible energy capacity, because it is the energy that would be delivered only in high, may be particularly profitable. An SU(t) profile that the case of reversible reactions. supplies just the peaks of the grid consumption—but not the

This journal is ª The Royal Society of Chemistry 2012 Energy Environ. Sci., 2012, 5, 7151–7160 | 7157 Fig. 6 Examples of possible supply profiles. (A) A typical normalized grid demand profile (same as in Fig. 1). (B) The same demand with the baseload subtracted to produce a grid minus baseload (GMB) scenario (red), plotted along with the normalized grid demand (gray) for reference. (C) A 5-hour square wave (SW) supply profile centered around the daily peak power consumption. baseload power—could represent a synergistic scenario in which In the real world, the supply scenario does not need to be intermittent renewable production, combined with a low-carbon predetermined indefinitely into the future. It may be varied to baseload production such as nuclear, utilizes electricity storage reflect changes in market conditions. A producer could to provide a carbon-free electricity mix. suddenly have some new transmission become available, and We studied three disparate scenarios in order to investigate the decide to change from the transmission-utilization-maximizing variability of the storage system power and energy requirements CONS profile to a presumably more profitable supply profile with varying SU(t). The first is the wind- and solar-to-constant such as SW. (CONS) scenario described previously. The second is a grid- From Fig. 7 we see that the type of production matters much minus-baseload (GMB) scenario, in which the minimum power more for the storage energy requirements than does the supply consumed is subtracted from the grid profile, as shown in scenario. The power required to reach a given efficiency, Fig. 6B. The third is a square wave (SW), 5 h in peak width, however, depends more significantly on the supply scenario than centered on the daily consumption peak, as shown in Fig. 6C. We on the production type. We conjecture that this trend is likely to expect these three cases to provide a sufficiently diverse set of remain valid for all other reasonably desirable supply scenarios. circumstances to provide an idea of how important SU(t) is to the With this observation we hypothesize some generalizations storage requirements. For each of these cases, we calculated both regarding storage for wind and solar electricity. First, with the power and energy requirements for a range of system effi- regard to energy requirements, mapping 1 MW of solar power ciency values. Diminishing returns at high efficiency are rapidly with the production characteristics of Fig. 1B onto any desirable reached in all cases, as the more detailed results in Fig. 5 showed supply scenario requires between about 12.5 and 25 MW h of for the CONS scenario. For this reason, we present only the energy storage capacity (about 0.5–1 days worth of peak power power and energy requirements for system efficiencies havg production capacity). Mapping 1 MW of wind power with the ranging from 95% down to 70% in increments of 5%. Fig. 7 production characteristics of Fig. 1A onto any desirable supply shows the calculation results for the CONS, SW, and GMB scenario requires between about 47.5 and 57.5 MW h of energy supply scenarios. storage capacity (about 2–2.5 days of nameplate power All the results for the wind production scenario are grouped production capacity). higher in required storage energy than those for the solar The required storage power is sensitive to the specified system production scenario. The SW supply scenario requires the most efficiency. If we focus on havg ¼ 85% as a reasonably practical power to reach 95% system efficiency for both wind and solar goal for the system efficiency, we observe that reaching this goal production profiles. Supplying the CONS scenario requires for 1 MW of either wind or solar PV peak power production approximately the same power and energy capacity as supplying requires roughly 2 MW or less of storage discharge power the GMB scenario. capacity, depending on the specific supply scenario.

7158 | Energy Environ. Sci., 2012, 5, 7151–7160 This journal is ª The Royal Society of Chemistry 2012 required in the speciﬁc supply scenario, i.e. MAX(ST(t)) # PA.

The Ploss(t) versus PA curve terminates when this inequality is violated. Certainly it is possible to run at lower efﬁciency by running at a current density past the value for maximum power, but doing so would achieve lower efﬁciency and lower power, making such operation useless.

4.3 Solid electrode batteries for wind or solar? It is interesting to compare the power-energy relationship for typical solid-electrode secondary batteries to the requirements for storing wind and PV electricity. These batteries typically have the characteristic that the power capacity and energy capacity scale together. Nickel metal-hydride batteries, for example, have a specific power of about 600 W kg1, and a specific energy of about 55 Whr kg1, resulting in an energy to power ratio of roughly 0.1 h, or 6 min: this corresponds to the discharge time if discharge power could remain at its peak value throughout the process. Similarly, the energy to power ratio of lead acid batteries is roughly 0.2 h, or 12 min, and that of lithium ion batteries is 0.6 h, or 35 min. This ratio defines a sloped line through the origin in a power versus energy plot. Moving along the line to larger powers and energies can be thought of as installing larger batteries, or more of them. Plotted along with the storage requirements in Fig. 7A are three sloped lines representing the energy to power ratio of NiMH, lead acid, and lithium ion batteries. They are difficult to interpret, because on this scale the lines are nearly vertical. Fig. 7B shows the exact same plot except the vertical axis has been rescaled by a factor of 100. Now the batteries’ energy to power ratios can be observed and compared readily, but the storage requirements have merged with the horizontal axis. We Fig. 7 (A) Power and energy requirements, normalized to peak wind or conclude that solid-electrode batteries store about two orders of PV production capacity, for several supply scenarios. All the results for magnitude too little energy when their power is matched to the the solar PV are grouped to the left below 25 h. All the results for wind are storage requirements for wind and solar PV. This does not mean grouped to the right near 50 h. In different colors are the different SU(t) they cannot do the job; on the contrary, if one bought enough scenarios; SW in pink, GMB in red, and CONS in blue. The highest point battery energy to serve one of these storage scenarios, the on each line corresponds to 95% system efficiency, and the efficiency batteries would be so vastly overpowered—by two orders of decreases in 5% increments with each successive point downwards. (B) The same exact data plotted with a vertical axis scale, showing the vast magnitude—that the efficiency would be essentially 100%. The difference in power scales between common solid-electrode batteries and cost of such an overpowered storage system has kept it from intermittent renewable electricity storage requirements. The same lines broad implementation so far. appear nearly vertical in (A) and are unlabeled. Flow batteries and regenerative fuel cells have a significant advantage in this regard. The power and energy capacities of these systems are separate engineering choices. The power A few representative calculations performed with other wind capacity is set by the cell hardware, which is typically the or solar PV production profiles indicate that these generaliza- expensive part. The energy capacity is set by the amount of tions seem to remain applicable as long as the production reactant and product and the size of their storage tanks one buys. capacity factors remain unchanged at 14% for PV and 32.5% for Because of this decoupling, one may independently size the wind. An interesting direction for future research is to investigate power and energy subsystems to be appropriate for the desired the sensitivity of these generalizations to variations in capacity scenario. For example, if the intention were to map 1 MW solar factor. A large number of wind and solar datasets for many production with 14% capacity factor onto a constant output at locations, which would be very useful in broadening this analysis, 85% efficiency, one would need to buy roughly a 0.5 MW are publicly available for download from www.NREL.gov. regenerative fuel cell; to provide the same service, one would Note that not all system efficiencies are attainable. For have to buy 87.5 MW of lead acid batteries. example, in Fig. 5A, the two curves terminate at low power instead of extending all of the way down to the origin. As the 5 Summary and conclusions maximum storage discharge power is decreased, the efficiency decreases. But the maximum discharge power can be decreased With sufficient electricity storage capacity, any power produc- only to the point that it reaches the maximum discharge power tion profile may be mapped onto any desired supply profile. We

This journal is ª The Royal Society of Chemistry 2012 Energy Environ. Sci., 2012, 5, 7151–7160 | 7159 have presented a detailed framework describing how to calculate Solid-electrode batteries are shown to have two orders of the required storage power as a function of time, for any given magnitude too little energy to power ratio to be well suited to power production profile, chosen supply profile, and targeted storage of intermittent renewables. For both wind and PV, for all system efficiency, accounting fully for the loss characteristics of the different supply scenarios studied, installing 1 MW of storage the storage system. For constant-activity electrochemical cells, discharge capacity for 1 MW of peak production yields system such as the regenerative hydrogen-chlorine fuel cell, a linear efficiencies of 70%–90%. approximation of the cell potential versus current density allows the entire efficiency behavior of the system to be described by a single scalar figure of merit—the maximum discharge power Acknowledgements P A, given by eqn (14). The parameterization in terms of the This research was supported by National Science Foundation maximum discharge power of other, non-electrochemical, grant NSF-IIP-0848366 through Sustainable Innovations, LLC. constant-activity energy storage systems exhibiting nearly linear response may be an equally valuable simplification of their analyses. References We considered three disparate supply scenarios; constant, 1 I. P. Gyuk and S. Eckroad, EPRI-DOE Handbook Supplement of grid-minus-baseload, and square wave, and two different Energy Storage for Grid Connected Wind Generation Applications, production scenarios; wind with a capacity factor 32.5%, and PV technical Report 1008703, EPRI and DOE, 2004. with a capacity factor of 14%. For each of these six combinations 2 Joseph F. DeCarolis and David W. Keith, The economics of large- scale wind power in a carbon constrained world, Energy Policy, of scenarios, we found the storage energy and power capacity 2006, 34, 395–410. requirements for a range of system efficiencies. We found 3 Koninklijk Nederlands Meteorologisch Instituut. KNMI HYDRA diminishing efficiency returns on increasing the maximum project website. 4 J. W. Verkaik, Evaluation of Two Gustiness Models for Exposure discharge power, as would be expected as one approaches 100% Correction Calculations, J. Appl. Meteorol., 2000, 39, 1613–1626. efficiency. The storage discharge power capacity requirement for 5 General Electric webpage containing turbine specifications. a given system efficiency is not very sensitive to variations in the 6 NREL PVWatts solar data for Boston, Massachusetts, 2009. type of power production (wind vs. solar PV), as shown in Fig. 7. 7 The National Grid webpage where one may download grid consumption data. The required power capacity increases rapidly with increasing 8 B. Parsons, M. Milligan, B. Zavadil, D. Brooks, B. Kirby, efficiency at the high-efficiency end, as shown in Fig. 5, illus- K. Dragoon and J. Caldwell, Grid Impacts of Wind Power: A trating the diminishing returns associated with over-sizing Summary of Recent Studies in the United States, technical report, storage power capacity. NREL, 2003. 9 John P. Barton and David G. Infield, Energy storage and its use with The storage energy capacity requirement for a wind produc- intermittent renewable energy, IEEE Trans. Energy Convers., 2004, tion scenario is much more demanding than for a PV production 19, 441–448. scenario with the same peak production power. The energy 10 Warren Katzenstein and Jay Apt, Air emissions due to wind and solar power, Environ. Sci. Technol., 2009, 43, 253–258. requirement is insensitive to the chosen supply scenario or the 11 J. Apt, The spectrum of power from wind turbines, J. Power Sources, system efficiency, for the range of system efficiencies studied 2007, 169, 369–374. (70%–95%). Most of the increased energy demand for wind 12 Jason Rugolo, Electricity Storage and the Hydrogen-Chlorine Fuel storage arises from the higher capacity factor of wind compared Cell, PhD thesis, Harvard University, 2010. 13 Bottling Electricity: Storage as a Strategic Tool for Managing to that of PV, but some of the increase arises from the charac- Variability and Capacity Concerns in the Modern Grid, technical teristic long periods during which the wind is still. report, The Electricity Advisory Committee, DOE, December 2008.

7160 | Energy Environ. Sci., 2012, 5, 7151–7160 This journal is ª The Royal Society of Chemistry 2012